Method and apparatus for minimizing the number of samples needed to determine cell radius coverage contour reliability in a radiotelephone system

ABSTRACT

A robust method for determining the boundaries of cells and the associated reliability of the RF coverage within these boundaries is presented. The invention accurately determines the average range from the base station to the cell edge from RF signal strength measurements with a linear regression approach. The accuracy of this estimate is quantified both as a range uncertainty (e.g. ±100 meters) and as a cell coverage reliability (i.e. area/edge) through 1) simulation, 2) analysis of real data, and 3) theoretical analysis. It is shown that if the estimate of the cell radius meets the desired accuracy, then the corresponding estimates of coverage reliability (both area and edge) are more than sufficiently accurate. It is recommended that radio survey analyses incorporate this test as part of the coverage validation process.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to wireless communications andin particular to cellular telephony.

2. Description of the Related Art

Frequently wireless network designers and equipment suppliers are taskedwith providing reliability estimates for coverage of cellular systems.Service providers want to know how reliable their coverage is and wantto be able to offer more reliable service to their customers.

Two standard ways to express cell reliability are illustrated in FIG. 1.They are contour (or cell edge) reliability as illustrated in FIG 1a,which gives the reliability of a user who travels the contour of thecell edge; and cell area reliability as illustrated in FIG. 1b, whichgives the reliability of a user who may be anywhere within the confinesof the entire cell boundary--not just on the cell edge. Both standardsare often specified by a user or service provider.

The coverage probabilities requested by a user typically range from 70%to 99%. For example, public safety users generally require 95% contourreliability which corresponds to no more than a 5% failure within theentire coverage area. Commercial users may be satisfied with 70% contourreliability which translates to a 90% reliability across the entire cellarea.

Previous designers were required to perform extensive RF measurements toestablish cell boundary and reliability figures of merit. Typically,field engineers would drive the cell area collecting data with aReceived Signal Strength Indicator (RSSI) receiver for measuring thereceived signal strength from a central transmitter. The exact locationof the receiver is known through Global Positioning System (GPS)receivers attached to the RSSI receiver. The previous systems andmethods for estimating cell coverage and reliability used hundreds andthousands of data points and still came up with estimates that rangedwithin plus or minus ten percent of actual (later) measurements werereluctantly considered acceptable.

The well known Hata method for estimating path loss is inherentlyerror-prone and is valid over only a very limited range under certainspecific conditions. A different correction factor is needed each andevery time the method is used. The correction factor may be determinedfor either a small, medium or large sized city and does not take intoaccount features of the particular cell under study. The unreliabilityis magnified if used to calculate cell radius and/or reliability.

There is accordingly a need for a new method and apparatus for reliablymeasuring and predicting the boundary of a cell and for the coveragewithin the cell in order to solve or ameliorate one or more of theabove-described problems.

SUMMARY OF THE INVENTION

An accurate computer implemented method and apparatus for measuring andpredicting the RF coverage of single cells is presented. The methodmeasures the distance from the base station to the cell edge andquantifies the accuracy by also specifying a range uncertainty. Inaddition, the method provides an estimate of the area reliability of theregion which is an order of magnitude more accurate than otherapproaches that estimate the coverage from a proportion of signalstrength measurements. Empirical formulas are given that approximate theinaccuracies of both of these estimates.

Since the method uses linear regression to estimate the minimum meansquare path loss to the cell edge, the technique represents the bestcircular approximation to the actual cell edge contour. As such, themethod is ideal for cell site planning with omni directional antennas.However, the approach can easily be modified to provide equally validcoverage measurements for sectorized cell sites. This invention appliesto any wireless technology to accurately determine the range to desiredcontours that satisfy the required RF coverage criterion. For example,using standard CW drive test measurements, this technique can helpverify that the RF design meets the proper amount of overlap in coverageneeded to support the soft hand-off regions of CDMA.

The minimum cell area that must be driven to validate the RF coveragecan be calculated from three major cellular design parameters: 1) theamount of lognormal fading in the cell, 2) the desired cell edgeuncertainty, and 3) the cell radius.

The limiting factor in determining the quality of RF cellular coverageis the accuracy that is required to estimate the effective cell radius.Estimates of the effective radius of each cell may be included as partof the pre-build validation procedure for any wireless installation.

An object of the invention is to determine the number of signal strengthmeasurements needed to accurately estimate the cell radius R from thebase station to the cell edge for both a given cell contour and cellarea reliability. A further object of the invention is to estimate thecoverage reliability of a cell with a finite number of signal strengthmeasurements. A still further object of the invention is to minimize thearea from which samples are taken in estimating cell radius R.

Further features of the above-described invention will become apparentfrom the detailed description hereinafter.

The foregoing features together with certain other features describedhereinafter enable the overall system to have properties differing notjust by a matter of degree from any related art, but offering an orderof magnitude more efficient use of processing time and resources.

Additional features and advantages of the invention will be set forth inpart in the description which follows, and in part will be apparent fromthe description, or may be learned by practice of the invention. Theadvantages of the invention will be realized and attained by means ofthe elements and combinations particularly pointed out in the appendedclaims.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not restrictive of the invention, as claimed.

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate preferred embodiments of theapparatus and method according to the invention and, together with thedescription, serve to explain the principles of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1a illustrates a contour reliability diagram of a wireless systemwith a typical cell edge reliability of 95%.

FIG. 1b illustrates an overall area reliability diagram of a wirelesssystem with a typical area reliability of 95%.

FIG. 2 illustrates an optimized mobile switching system architecture ofthe present invention.

FIG. 3a illustrates the approach to best approximating the actual cellcontour.

FIG. 3b illustrates the range to cell edge and corresponding rangeuncertainty ring ΔR.

FIG. 4 illustrates a graphical approach to estimating cell radius R.

FIG. 5 illustrates a computer system of the present invention includinga linear regression engine for estimating parameters for cell radiuscalculation.

FIG. 6 illustrates in flowchart form a general method for calculatingcell contour and edge reliability.

FIG. 7 illustrates in flowchart form a method for minimizing the numberof measurement points required for calculating cell reliability.

FIG. 8 illustrates in flowchart form a method for minimizing the areafrom which a number of measurement points are required for calculatingcell reliability.

FIG. 9a illustrates histogram of the relative probability densities ofcell reliability estimates for contour and edge reliability for 75% celledge reliability.

FIG. 9b illustrates histogram of the relative probability densities ofcell reliability estimates for contour and edge reliability for 90% celledge reliability.

FIG. 10a illustrates range inaccuracy for a 75% cell edge reliability.

FIG. 10b illustrates coverage inaccuracy for a 75% cell edgereliability.

FIG. 10c illustrates range inaccuracy for a 90% cell edge reliability.

FIG. 10d illustrates coverage inaccuracy for a 90% cell edgereliability.

FIG. 11 illustrates an accuracy comparison between cell radius estimateand area reliability estimate.

FIG. 12a illustrates the typical drive route in a small cell.

FIG. 12b illustrates the typical drive route in a large cell.

FIG. 13 illustrates the percentage area of a cell that must be sampledfrom to verify RF coverage.

DETAILED DESCRIPTION

Referring now to FIG. 2, an optimized mobile switching systemarchitecture 200 of the present invention is disclosed. A mobileswitching center (MSC) 204 serves to connect the public telephonenetwork 202 to optimally designed cells 212-218. Each cell 212-218includes a base station 208 located within its boundary forcommunicating via radiowaves with a number of mobile stations 206. Eachoptimally designed cell has a radius R 210 that is particular to thespecific cell 212-218.

FIG. 3a illustrates the measurement method of the instant invention. Thecontour of a cell is estimated based on a sampling of received data. Theactual contour of the cell 304 is compared to a circle 302 of radius R306.The resulting actual cell contour 310 is quantified in terms of aRange Uncertainty Ring 310 of R plus or minus ΔR.

The accuracy of the estimate of the distance to the cell edge isquantified in terms of a range uncertainty ring, ±ΔR, as shown in FIG.3b, where ΔR is expressed as a percentage of the total cell radius, R.For 500 signal strength measurements, simulations show that ΔR≈6.5% ofthe cell radius, which for a 2 km cell radius yields a range uncertaintyof ±ΔR≈±130 meters. The accuracies of both the range and coverageestimates increase with increases in the number of signal strengthsamples processed.

Two methods for determining coverage reliability from drive test dataare compared. The first method is the standard approach of estimatingthe proportion of signal strengths that are above a desired reliabilitythreshold as illustrated in Hill, C. and Olson, B., "A StatisticalAnalysis of Radio System Coverage Acceptance Testing," IEEE VehicularTechnology Society News, Feb. 1994, pp. 4-13 and is hereby incorporatedby reference. This method is shown to be much less accurate than thesecond approach, producing estimates that are easily biased by thenonuniform sampling commonly found in drive test data.

The second approach is the preferred method of the invention. Thismethod involves determining the propagation parameters of individualcells and using this information in conjunction with the analysis byReudink, D. O., Microwave Mobile Communications, edited by Jakes, W. C.,IEEE Press, reprinted 1993, ISBN 0-7803-1069-1, Chapter 2, pp. 126-128,which is herein incorporated by reference, (see equation (a7) in theAppendix) to estimate the coverage reliability. The propagation path isapproximated by a two-parameter model similar (in appearance only) toHata. A fade margin based on the actual signal variation within eachcell is calculated to ensure the desired cell edge reliability. Thistechnique provides much more accurate coverage estimates which arenearly independent of the spatial location of the signal strengthsamples. This method estimates the best circular boundary that matchesthe cell edge contour at the desired reliability, as illustrated in FIG.3a. An advantage of this approach is that an accurate estimate of thecoverage reliability can be made without driving 100% of the cell area.Simulations show that, for cells designed with 75% cell edgereliability, the coverage error is less than 0.5% with as few as 500signal strength measurements and for 90% cell edge designs the error isless than 0.2%.

Typically, cell radius estimation and area reliability analyses are notconsidered together in propagation optimization. These two problemscannot be considered independently, and the consequence of doing so canlead to inaccurate estimates of RF performance.

The proposed approach for estimating the cell radius is graphicallysummarized in FIG. 4. Item 400 graphically represents all driveable areaaround a base station, both within and external to a cell boundary. Theareas denoted by rectangles 402 and 404 represent the area within theboundary of a cell of Radius R 412.The received signal level (RSL) isplotted as a function of the logarithm of the distance from thebasestation transmitter. Mean path loss is represented by line 406. Afade margin to account for other attenuation is built in to themeasurement method. When an RSL falls above a predetermined thresholdP_(THRESH) 410 then the range presumably is within the cell radius. Whenan RSL falls below predetermined threshold P_(THRESH) 410 then thelocation is used to determine the value of R for a given desired contourreliability.

Area reliability is graphically determined by dividing the number ofreceived signal points N1 above threshold P_(THRESH) 410 by the sum ofN1 and the number N2 of received signal points; i.e.Reliability=N1/(N1+N2). Radius R is then adjusted in order to have theReliability calculation meet its desired target.

The measurement method for determining radius R as a function of cellcontour reliability is based on a two parameter propagation modelsimilar to the prediction formulas of Hata, where

    P.sub.r =P.sub.t -P.sub.L =P.sub.t -A-Blog.sub.10 r        (1)

where P_(r) is the received power (dBm), P_(t) is the EIRP of the basestation plus the receiver gain (e.g. P_(t) =50 dBm EIRP+G_(r)), P_(L) isthe path loss (dB), r is the range (km) from the base station, and A andB are the unknown constants to be estimated from the RF data via linearregression as illustrated in FIG. 5. A fade margin based on the actualsignal variation within each cell is calculated to ensure the desiredcell edge reliability.

Because of the similarity in appearance to Hata's model, it is importantto clarify that the method does not incorporate Hata's coefficients.Both Hata and the instant invention utilize a linear approximationmethodology. Unlike Hata, in the instant invention, the salientpropagation parameters are estimated from the data since the goal inthis study is RF measurement, not RF prediction.

The signal strength data received 502 for each cell are first quantizedinto range bins of 100 meter resolution, where each bin represents anaverage power measurement at a certain range from the base station. Therange axis 504 is then mapped to a logarithmic (common log) scale, thetransmit power is combined with the received signal strength parameter,A, and the two parameters of the following equivalent model areestimated via linear regression in the equation

    P.sub.r =A'-Br.sub.L                                       (2)

where r_(L) =log₁₀ r and A'=P_(t) -A.

Once the constants A' 508 and B 510 have been estimated, the mean trendof the propagation data is subtracted from the signal strengthmeasurements and the standard deviation, σ 512 of the remainingzero-mean process is estimated. The value of σ 512 represents thecomposite variation due to two primary factors: lognormal fading andmeasurement error. Both of these factors tend to introduce uncorrelatederrors since the regression is computed for range measurements acrossall angles, which greatly reduces most spatial correlation effects.

A fade margin, FM₉₄ that ensures the desired service reliability, F(z),can then be approximated (see equation (a4) in Appendix)

    FM.sub.94 =z σ                                       (3) ##EQU1##

For example, cell edge reliabilities of 75% and 90% correspond to fademargins of about 0.675σ and 1.282σ, respectively. Slightly more preciseexpressions can be obtained by limiting the range of the fading to-4σ<z<2σ. However, this provides only a minor improvement in the fademargin estimate since the area under the tails of the Normal densityfunction is quite small.

It is now straightforward to derive the distance to the cell edge, R, atany desired signal strength threshold, P_(THRESH), and servicereliability, F(z). From equations (1), (2), (3), and (4)

    R=10.sup.-(P.sbsp.THRESH.sup.+FM.sbsp.σ.sup.-A')/B   (5)

Any additional static (nonfading) margin such as building penetrationlosses are also incorporated into the P_(THRESH) term. Thus, A',B and, σare all that is needed to determine the range from the base station tothe cell edge for a given desired cell contour reliability.

The methodology of determining cell radius in a computer 500 for a givendesired contour reliability is illustrated in flowchart form in FIG. 6.Flowchart 600 control begins in Start box 605. If the area to be sampledin a drive test is to be minimized, then Aminflag is the variable whichrepresents the status of the minimum geographic area traveled. It isinitially set to False, which indicates that the number of received datafrom a minimized travel area within a geographic region have yet to beinput. If the number of received data is to be minimized, then Nminflagis used to indicate the status of whether the minimum number of receiveddata have been input yet. This flag is also initially set to False andis represented in step 610.

In step 615, the received data is input. The received data comprisesrange and received signal level information. This information may beinput from computer memory, a receiver connected to an antenna forreceiving data transmitted from a base station or to any other externalsource and may be in real-time, near real-time or delayed in time. Theprocessing may occur in the field or a number of samples may be storedfor processing at a later time at another central or field location.

In step 620, control passes to step 625 if the number of received datais not to be minimized and an arbitrary number of received data are thenused. In any event, control is then passed to step 630 where theiterative process of generating the constants A' and B in the equationP_(r) =A'-Br_(L) by using linear regression is accomplished. Linearregression is the well-known technique of finding the best fit linearapproximation of a set of data points according to the equation y=mx+b;where b=A'=y-intercept, B=-m=slope (the slope is negative as would beexpected for a received signal which attenuates as distance from thetransmitter increases) and the logarithm of range r_(L) corresponds tothe independent variable x. For each received data the best fit line isrecalculated and will change from one iteration to the next.

The standard deviation a is calculated in step 635 by means as describedabove during the discussion of FIG. 5.

In steps 640 and 645 fade margins and cell radius are calculated as alsodescribed above during the discussion of FIG. 5 according to equations3), 4) and 5), respectively.

In step 650, an embodiment of the present invention allows for thecalling of a subroutine to minimize the number of received datanecessary for processing in calculating cell radius for a given level ofcontour reliability desired. This subroutine will be discussed later inreference to FIG. 7.

In step 655, another embodiment of the present invention allows for thecalling of a subroutine to minimize the geographic area from whichreceived data has been sampled. This feature allows a minimization oftime and expense in planning and executing an optimized drive test. Thissubroutine will be discussed later in reference to FIG. 8.

In step 660, the returned data from the subroutines is examined todetermine if analysis is completed by having the minimum number ofreceived data processed and/or minimized area from which received datahas been processed. If processing is complete, the program completesprocessing in step 670. If not, control loops back to step 630 and theprocess is repeated and the analysis is further refined.

Referring now to FIG. 7, the subroutine to minimize the number ofreceived data will be discussed. If the number of received data is notto be minimized as determined in step 710, then counter X is incrementedin step 715 and control is returned by step 720 to step 650 of theflowchart in FIG. 6. If the number of received data is to be minimizedas determined in step 710, then the maximum allowable percentage errorδR in cell radius is input in step 725. The error is calculated in step735 according to the equation δR=RΔR, where

    R=10.sup.-(P.sbsp.THRESH.sup.+FM.sbsp.σ.sup.-A')/B

and ##EQU2## for values of N samples. If δR does not fall below themaximum allowable predetermined target value, then control returns bystep 740 to step 650 of the flowchart of FIG. 6. If δR does fall belowthe maximum allowable error in step 735, then the variable Nminflag isset to True in step 745 and control returns by way of step 750 to step650 of the flowchart of FIG. 6.

FIG. 8 will now be discussed. Subroutine Minimize travel area begins instep 805 and passes control to step 810. If the received data is not tobe gathered from a minimized geographic area, then control transfersfrom step 810 to step 825 where the variable Aminflag is set to true.Variable Aminflag when set true indicates that the area traversed neednot be minimized at all or that it already has been minimized. Controlis returned by step 835 to step 655 of the flowchart of FIG. 6.

If the area to be traveled is to be minimized, then control passes fromstep 810 to 815 where Amin is calculated according to the equation##EQU3## and σ is the estimated standard deviation of the lognormalfading in the cell. In step 820, Amin is compared to the actual traveledarea and if the actual sampled area is greater than Amin, then controlis passed to step 825 where Aminflag is set true indicating that thereceived data originates from a large enough geographic area and controlreturns by step 835 to step 655 of the flowchart of FIG. 6. If theactual sampled area is less than Amin, then Aminflag remains set toFalse and control returns by step 830 to step 655 of the flowchart ofFIG. 6.

In another embodiment of the present invention, cell area reliability ismeasured and predicted.

The methodology of determining cell radius in a computer 500 for a givendesired cell area reliability is also illustrated in generic flowchartform in FIG. 6. The basic principles are analogous as described above inreference to cell contour reliability. Flowchart 600 control begins inStart box 605. If the area to be sampled in a drive test is to beminimized, then Aminflag is the variable which represents the status ofthe minimum geographic area traveled. It is initially set to False,which indicates that the number of received data from a minimized travelarea within a geographic region have yet to be input. If the number ofreceived data is to be minimized, then Nminflag is used to indicate thestatus of whether the minimum number of received data have been inputyet. This flag is also initially set to False and is represented in step610.

In step 615, the received data is input. The received data comprisesrange and received signal level information. This information may beinput from computer memory, a receiver connected to an antenna forreceiving data transmitted from a base station or to any other externalsource and may be in real-time, near real-time or delayed in time. Theprocessing may occur in the field or a number of samples may be storedfor processing at a later time at another central or field location.

In step 620, control passes to step 625 if the number of received datais not to be minimized and an arbitrary number of received data are thenused. In any event, control is then passed to step 630 where theiterative process of generating the constants A' and B in the equationP_(r) =A'-Br_(L) by using linear regression is accomplished. For eachreceived data the best fit line is recalculated and will change from oneiteration to the next.

The standard deviation σ is calculated in step 635 by means as describedabove during the discussion of FIG. 5.

In steps 640 fade margins are calculated as also described above duringthe discussion of FIG. 5 according to equations 3) and 4), respectively.

In step 645 cell radius R for a given cell area reliability iscalculated using the following equation and ##EQU4##

In step 650, an embodiment of the present invention allows for thecalling of a subroutine to minimize the number of received datanecessary for processing in calculating cell radius for a given level ofcell area reliability desired. This subroutine will be discussed laterin reference to FIG. 7.

In step 655, another embodiment of the present invention allows for thecalling of a subroutine to minimize the geographic area from whichreceived data has been sampled. This feature allows a minimization oftime and expense in planning and executing an optimized drive test. Thissubroutine will be discussed later in reference to FIG. 8.

In step 660, the returned data from the subroutines is examined todetermine if analysis is completed by having the minimum number ofreceived data processed and/or minimized area from which received datahas been processed. If processing is complete, the program completesprocessing in step 670. If not, control loops back to step 630 and theprocess is repeated and the analysis is further refined.

Referring now to FIG. 7, the subroutine to minimize the number ofreceived data will be discussed. If the number of received data is notto be minimized as determined in step 710, then counter X is incrementedin step 715 and control is returned by step 720 to step 650 of theflowchart in FIG. 6. If the number of received data is to be minimizedas determined in step 710, then the maximum allowable error ΔF_(u) incell radius is input in step 725. The error is calculated in step 735according to the equation ##EQU5## as described above for values of Nsamples. If the error does not fall below the maximum allowablepredetermined target value, then control returns by step 740 to step 650of the flowchart of FIG. 6. If the error does fall below the maximumallowable error in step 735, then the variable Nminflag is set to Truein step 745 and control returns by way of step 750 to step 650 of theflowchart of FIG. 6.

FIG. 8 will now be discussed with respect to minimizing sampling areawith respect to cell area reliability. Note that these calculations areequivalent to the calculations for cell contour reliability SubroutineMinimize travel area begins in step 805 and passes control to step 810.If the received data is not to be gathered from a minimized geographicarea, then control transfers from step 810 to step 825 where thevariable Aminflag is set to true. Variable Aminflag when set trueindicates that the area traversed need not be minimized at all or thatit already has been minimized. Control is returned by step 835 to step655 of the flowchart of FIG. 6.

If the area to be traveled is to be minimized, then control passes fromstep 810 to 815 where Amin is calculated according to the equation##EQU6## and σ is the estimated standard deviation of the lognormalfading in the cell. In step 820, Amin is compared to the actual traveledarea and if the actual sampled area is greater than Amin, then controlis passed to step 825 where Aminflag is set true indicating that thereceived data originates from a large enough geographic area and controlreturns by step 835 to step 655 of the flowchart of FIG. 6. If theactual sampled area is less than Amin, then Aminflag remains set toFalse and control returns by step 830 to step 655 of the flowchart ofFIG. 6.

The methodology illustrated in FIGS. 6-8 will now be discussed in moredetail as applied to both cell contour and cell area reliability.

A simulation is used to determine the probability densities of thefollowing two random variables: ##EQU7## where e_(Fu) is the relativeerror of the area availability estimate as computed from equation (a7);

e_(R) is the relative error of the estimate of the range to the celledge;

F_(u) is the true area reliability computed from equation (a7);

F_(u) is the estimated area reliability computed from equation (a7);

R is the true range to the cell edge computed from equation (5); and

R is the estimated range to the cell edge computed from equation (5).

Typical probability densities for e_(Fu) and e_(R) are shown in FIGS. 9aand 9b. Note that the error of the cell radius estimate, e_(R), iscomparable in FIG. 9a and 9b. However, e_(Fu) is almost a factor of twosmaller for the 90% cell edge reliability design. The histograms in FIG.9 illustrate that both e_(R) and e_(Fu) are well modeled as zero-meanNormal random variables, and thus, only their respective variances areneeded to characterize the accuracies of the estimates R and F_(u).These are determined empirically via Monte Carlo simulation.

The zero-mean properties of both e_(R) and e_(Fu) are nearly independentof the nonuniformities of finite sampling commonly found in drive testdata. That is, R and F_(u) are not easily biased by the data collectionprocess, giving these estimators a significant accuracy advantage oversimply estimating the reliability from a proportion of signal strengthvalues that are above a threshold. The main difference is that theregression does not directly estimate a probability but rather thepropagation parameters: A', B and σ of each cell. In addition, the areareliability, F_(u) from equation (a7), is a function of four variables:R, A', B and σ and thus does not depend as much on errors in R, as doesthe method of estimating RF reliability from a proportion of signalstrength values.

In determining the inaccuracy, ΔR, of the estimate of the cell radius ata 95% confidence level. The inaccuracy is measured from empiricalhistograms by simulating e_(R) and determining ΔR such that

    P(R-ΔR≦R≦R+ΔR)=95%

The inaccuracy of the range estimate, ΔR, is determined by the followingtwo-sided test ##EQU8## where the z_(c) variable in the above equationis chosen to yield the desired confidence level, c. For example, ifc=95%, then z_(c) =1.96. Since e_(R) has a mean of zero, thecorresponding two-sided range inaccuracy is ##EQU9##

Likewise, the inaccuracy of the area reliability estimate, F_(u), isestimated from histograms of e_(Fu) and determining ΔF_(u) such that

    P(F.sub.u ≦F.sub.u +ΔF.sub.u)=95%

Since e_(Fu) also has a mean of zero, the inaccuracy, ΔF_(u), (one sided95% confidence interval) of the coverage estimate is ##EQU10##

Each point in the accuracy plots in FIG. 10 represents the precision (at95% confidence) that is obtained after simulating and processing fivemillion signal strength values.

Note that 1000 samples in the regression are needed for about a ±3%inaccuracy in the cell radius estimate. However, even with 500 samplesin the regression, the area availability estimate is extraordinarilyaccurate. The inaccuracy is less than 0.5% for cells designed with 75%cell edge reliability and within 0.2% for cells designed with 90% celledge reliability.

The inaccuracies of both of the estimates R and F_(u) can beapproximated by the following expressions which were determinedempirically from the data in FIG. 10 with ##EQU11## where N is thenumber of samples in the regression;

σ is the estimated standard deviation of the lognormal fading in thecell; and

F_(u) is the estimated area reliability computed from equation (a7).

Note that the range inaccuracy in equation (6), ΔR, is inverselyproportional to the number of samples in the regression, N. Whereas, thearea reliability inaccuracy in equation (7), ΔF_(u), is inverselyproportional to the square root of the number of samples in theregression.

From equations (6) and (7) it may be seen that the area reliabilityestimate is much more accurate than the estimate of the cell radius.This is illustrated in FIG. 11 where the relative accuracy of these twoquantities is expressed as the ratio ΔR/ΔF_(u). The accuracy is computedfor two different area availability values (90% and 97%) and plotted asa function of the number of samples in the regression. Note that theestimate of the cell radius is more than ten times less accurate thanthe area reliability estimate for most of the situations of practicalinterest. The accuracy of the estimate of the cell radius (i.e.,equation (7)) is thus the limiting factor in determining the quality ofRF coverage over the cell area.

It is interesting to compare the magnitudes of the inaccuracies of theabove area reliability measurements with those computed by estimating aproportion of signal strength measurements that are above a desiredthreshold. For 500 samples and 90% cell edge reliability the inaccuracywas shown to be about 5.8%. Thus, the area availability estimated F_(u)presented in this study is more than ten times the accuracy of estimatesthat are based on a proportion of signal strengths.

Minimizing cell area to be sampled will now be further discussed.

The cell radius is the limiting factor in determining the reliability ofRF coverage. It was shown that the accuracy of the cell radius estimateis one of the major factors that determines the number of requiredsignal strength measurements. In this section, these results are appliedto the problem of determining the minimum percentage of area of a cellthat must be driven to verify that the RF signal strength coverage meetsa desired cell radius accuracy.

For the analysis that follows, it is assumed that the processing binsize for determining the signal power is 100 m×100 m and that themeasurements are taken at time intervals that result in independentsamples. Thus, fast fading effects are eliminated and variations insignal power are mostly due to lognormal fading. Equation (6) can beused to determine the minimum linear distance, D, that must be driven toachieve a desired accuracy in estimating the cell radius: ##EQU12##where it is assumed that drive routes are linear concatenations of 100m×100 m bins. For example, for ΔR =10%, and σ=8 dB, the minimum requireddistance is D=35 km (about 22 miles). For this case, independent of cellradius, about 22 miles of drive test data must be collected for a 10%error in the cell radius estimate (and a lognormal fading of 8 dB). Themain point is that for a desired inaccuracy in the estimate of the cellradius, ΔR, a fixed linear distance, D, must be driven independent ofthe actual cell radius, R. As illustrated in FIG. 12a, this results inthe requirement that small cells (e.g., R=1 km) must be driveneverywhere and sometimes overdriven. However, note that for large cells(e.g., R=30 km, FIG. 10b) often only a few primary roads need be to bedriven. Note that the scale in FIG. 12a is magnified about 13 times thatof FIG. 12b. Also, in FIG. 12 it is assumed that ΔR=5%, σ=8 dB, and D=70km (about 44 miles).

Thus, equation (8) specifies the theoretical minimum length of aparticular drive route, D. The actual length required for real drivetests will be longer. For example, in many small cells it is unlikelythat a contiguous drive route of length, D, exists. Also, for largecells the objective may be ubiquitous coverage rather than coverage ofprimary roads, requiring additional driving. Although these effects leadto drive routes that are somewhat longer than D, they do not diminishthe importance of equation (8) as a lower bound.

Alternatively, the minimum area of a cell that needs to be drive testedfor a given cell edge accuracy can also be determined. The number ofindependent 100 m×100 m bins in a cell of radius, r, is ##EQU13##

Since the number of required measurements is primarily governed by theaccuracy of the cell edge estimate, equation (9) can be equated withequation (6) to determine the minimum percentage of area that must besampled. This percentage is found by first solving for the minimumrequired radius of samples ##EQU14##

The radius in equation (10) defines the minimum circular area, πr², thatmust be driven to achieve a desired cell edge accuracy. For example, ifthis area is greater than or equal to the area of the cell, πR² (where Ris the cell radius), then additional drive test samples must be takenoutside of the cell. This is not a problem since the inventionaccommodates the additional required bins outside of the boundary of thecell. However, if πr² is greater than the area of the cell (πR²), the Nbins defined by equation (6) can be entirely contained within the cell.

Thus, the minimum percentage of area of a cell that must be driven tovalidate the RF coverage is ##EQU15## where σ is the estimated standarddeviation of the lognormal fading in the cell;

P is the cell radius (km);

ΔR is the inaccuracy of the estimate of the cell radius as specified inequation (6); and

r (km) is the minimum required radius of samples determined fromequation (10).

Some results for typical cell radii are illustrated in FIG. 13. Thequantity A_(min) is chosen as the ordinate and plotted on a logarithmicscale to emphasize the differences in the curves. The abscissa in thisfigure is cell radius, R (km), and the parameter associated with eachcurve is the desired inaccuracy of the cell radius estimate in meters,δR=R ΔR. For this figure it is assumed that σ=8 dB and that themeasurement bin size is 100 m×100 m. The upper curve is approximatelythe lower limit of the cell edge accuracy, since an uncertainty of ±50 mcovers the expanse of a single 100 m measurement bin. Note that forlarge cells only a small fraction of the cell area needs to be driven.For example, for an inaccuracy of ±ΔR=±150 m and a cell radius of 15 km,only 5% of the cell area must be driven. However, for small cells andhigh accuracy in the cell edge estimates, a significant number of drivetest samples must be taken outside of the cell's radius. For example,for ±ΔR=±50 m, a cell with a 1 km radius must be overdriven by apercentage of area of about 222%. The results shown in FIG. 10 and FIG.11 can be used to develop strategies that help minimize the time andmoney spent in drive testing cellular networks.

Equations (8) and (11) are important since they relate the minimumrequired distance and the minimum required cell area that must be drivento validate RF signal strength coverage to three major cellular designparameters: 1) the amount of lognormal fading in the cell, σ; 2) thedesired cell radius uncertainty, ΔR ; and 3) for the case of determiningthe minimum required cell area, the cell radius, R.

The following summarizes the above results in a guideline that can beused to help select productive drive routes:

1. Select an acceptable level of inaccuracy, ΔR, in the cell radiusestimate. Typical values are in the range of 5% to 10% (of the cellradius). Choosing values smaller than 5% can lead to drive routes thatare unnecessarily long. Choosing values much larger than 10% may lead tounacceptable levels of error in RF coverage.

2. Estimate the minimum distance, D, that must be driven to validate theRF coverage from equation (8). Note that this distance is the same ineach cell, regardless of the cell radius.

3. Estimate the required "density" of signal strength measurements. Auseful metric of sampling density is the minimum percentage of cell areathat must be driven, A_(min), shown in FIG. 13 and equation (11). Notethat A_(min) is primarily determined by the estimate of cell radius, aswell as the desired inaccuracy, ΔR. However, other factors such as thecomplexity of the propagation environment, projected traffic, etc., canalso affect the density of required RF measurements. All of thesefactors directly influence the orientation of the drive routes byconstraining them within areas that must be: (a) heavily drive tested(b) moderately drive tested or (c) lightly drive tested.

4. Select a key number important road segments within the cell whosecombined lengths add up to the minimum required drive distance, D,defined in equation (8). If ubiquitous coverage is the objective, themajority of signal strength measurements should be taken in the vicinityof the cell edge (both inside and, if necessary, outside of the celledge). In benign propagation environments, there is generally not muchto be gained by driving in the direct vicinity of the base station(e.g., within 50% of the cell radius) since this area produces fewsignal strength outages.

If the cell is small (e.g., R<2 km), it is likely that the entire cell'sarea is important. For small cells, it is also likely that the length ofall of the road segments within the cell will not be sufficient to meetthe minimum drive distance requirement, D. For these cases, signalstrength samples must be taken outside of the cell boundary. Identify asmany key areas internal to the cell as possible and make sure they areadequately represented in the drive test. The remaining required signalstrength samples should then be taken outside of the cell, as close aspossible to the cell edge.

In contrast, for large cells (e.g., R>10 km), only a few key highwaysmay be important and these should be heavily drive tested. For largecells there are usually more than enough road segments within the cellto meet the minimum drive distance requirement, D. After sampling thekey highways, any remaining required measurements should then berandomly collected from within the cell, preferably near the cell edge(i.e., hand-off areas). In large cells, it is generally unnecessary tocollect measurements significantly beyond the cell boundary.

Other such embodiments of the invention will be apparent to thoseskilled in the art from consideration of the specification and practiceof the invention disclosed herein. It is readily apparent that the abovedescribed invention may be implemented in any type of radiocommunication system including any cellular system. It is intended thatthe specification and examples be considered as exemplary only, with atrue scope and spirit of the invention being indicated by the followingclaims.

                  APPENDIX A                                                      ______________________________________                                        RELATIONSHIP BETWEEN CELL EDGE                                                AND CELL AREA RELIABILITY                                                     ______________________________________                                        Let the received power, P.sub.r, at the edge of a                             cell, R, be given by                                                          P.sub.r (R) = A' - Blog.sub.10 R + X                                                                        (a1)                                            where X is a normal zero mean random variable                                 with variance s.sup.2.                                                        Similarly, the received power at a distance, r,                               is P.sub.r (r) = A' - Blog.sub.10 r + X                                                                     (a2)                                            where it will be assumed that r < R. The outage                               probability, P.sub.out (r), at a particular range, r, from the                base station is given by                                                      1 #STR1##                     (a3)                                            and the corresponding service reliability is                                  2 #STR2##                     (a4)                                            where P.sub.THRESH is the desired threshold and                               Q(x) = 1 - Q(-x)                                                              Q(x) = 1 - F(x)                                                               F(x) = P(ξ ≦ x)                                                     ξ ≈ N(0,1)                                                         3 #STR3##                                                                     4 #STR4##                                                                     Define                                                                        5 #STR5##                                                                     6 #STR6##                                                                     Then from equation (a4), the edge reliability on                              a contour of range, r, is                                                     1 - P.sub.out (r) = Q(a + blnr)                                                                             (a5)                                            The fraction of usable area, F.sub.u, (i.e., area                             reliability) within the cell can be found by integrating                      the contour reliability across range                                          7 #STR7##                     (a6)                                            Now consider the integral                                                     8 #STR8##                                                                     set                                                                           t = a + blnr                                                                  9 #STR9##                                                                     0 #STR10##                                                                    Thus                                                                          1 #STR11##                                                                    Now                                                                           2 #STR12##                                                                    3 #STR13##                                                                    4 #STR14##                                                                    5 #STR15##                                                                    6 #STR16##                                                                    Thus, the area reliability is                                                 7 #STR17##                                                                    And finally,                                                                  8 #STR18##                    (a7)                                            ______________________________________                                    

What is claimed is:
 1. A method of determining, with a predetermined radius inaccuracy ±ΔR and with a minimum number of signal power value measurements, the radius R of a cell of a wireless communication system, wherein ΔR is a percentage of R, said wireless communication system including a base station transmitter, said method comprising the steps of:a) measuring a signal power value at a location a distance r from said transmitter; b) estimating the standard deviation σ of lognormal fading of said measured signal power values; c) computing a radius inaccuracy Δr from the number n of measured signal power values and said standard deviation σ; and, d) repeating steps a) through c) at different locations until Δr is equal to or less than ΔR.
 2. The method of claim 1 further including the step of:determining the radius R of the cell based on power received at a distance r from the transmitter calculated from the equation P_(r) =A'-Br_(L) ; wherein the parameters A' and B are estimated using a predetermined methodology, wherein P_(r) is the measured received power for a given location and r_(L) is log₁₀ r.
 3. The method of claim 2 wherein the predetermined methodology for estimating A' and B is linear regression analysis with said received data as inputs.
 4. The method of claim 3 wherein said step of estimating said standard deviation σ includes the step of:subtracting the received the data from the linear regression generated mean trend of the received data.
 5. The method of claim 4 further including the step of:calculating a fade margin FM.sub.σ based on a predetermined target reliability figure F(z) and said standard deviation σ.
 6. The method of claim 5 further including the step of:calculating the fade margin FM.sub.σ by using the equation FM.sub.σ =zσ, wherein z is calculated ##EQU16##
 7. The method of claim 6 wherein: said radius R of the cell is based on a function of the fade margin FM.sub.σ, a minimum received acceptable signal strength P_(THRESH), A' and B.
 8. The method of claim 7 wherein:said radius R is calculated by using the equation

    R=10.sup.-(P.sbsp.THRESH.sup.+FM.sbsp.σ.sup.-A')/B.


9. The method of claim 1 wherein said radius inaccuracy Δr is calculated according to the equation ##EQU17## wherein n is the number of signal power level values received.
 10. A method of determining the minimum number N of signal level values to determine the radius R of a cell of a wireless communication system with a radius inaccuracy of ±ΔR, wherein ΔR is a percentage of R, said cell including a base station transmitter, said method comprising the steps of:measuring signal power level values at a plurality of locations; estimating the standard deviation σ of lognormal fading for said measured signal power level values; and, computing said minimum number N based upon said standard deviation σ and said radius inaccuracy ΔR.
 11. The method of claim 10 further including the step of:determining the radius R of the cell based on power received at a distance r from the transmitter calculated from the equation P_(r) =A'-Br_(L) ; wherein the parameters A' and B are estimated using a predetermined methodology, wherein P_(r) is the measured received power for a given location and r_(L) is log₁₀ r.
 12. The method of claim 11 wherein the predetermined methodology for estimating A' and B is linear regression analysis with said received data as inputs.
 13. The method of claim 12 wherein said step of estimating said standard deviation σ includes the step of:subtracting the received data from the linear regression generated mean trend of the received data.
 14. The method of claim 13 further including the step of:calculating a fade margin FM.sub.σ based on a predetermined target reliability figure F(z) and said standard deviation σ.
 15. The method of claim 14 further including the step of:calculating the fade margin FM.sub.σ by using the equation FM.sub.σ =zσ, wherein z is calculated ##EQU18##
 16. The method of claim 15 wherein: said radius R of the cell is based on a function of the fade margin FM.sub.σ, a minimum received acceptable signal strength P_(THRESH), A' and B.
 17. The method of claim 16 wherein:said radius R is calculated by using the equation

    R=10.sup.-(P.sbsp.THRESH.sup.+FM.sbsp.σ.sup.-A')/B.


18. The method of claim 10 wherein said minimum number N is calculated according to the equation ##EQU19## 